A New Scheme for ChaoticAttractor-Theory Oriented Data
Assimilation
Jincheng Wang and Jianping Li
LASG, IAP
Email: [email protected]
University Allied Workshop, Japan, 2008
Contents
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1. Introduction
2. A new scheme 4DSVD for CDA
3. Comparison of 4DSVD and 4DVAR
4. Some OSSEs using WRF model
5. Conclusions and Discussions
Introduction
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Disadvantages of the traditional data assimilation (DA) methods
EnKF
4DVAR
1. Adjoint Model
1. Initial ensemble
TEXT
2. Large computation
time
2. Difficult to match
4DVAR performance
3. Background error covariance matrix

Chaotic-Attractor Oriented DA (CDA) theory


(Qiu and Chou, 2006)
To reduce the dimension of the DA problem
Consider the Characteristics of the Atmospheric model




The chaotic attractor of the atmospheric model exists
Its dimension is much smaller than the degree of the model space
The attractor could be embedded into space R2S+1
DA problem can be solved in the attractor phase space
The new scheme 4DSVD for CDA
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1. Generate samples
xif, j  M ti ,t j [xi ]
X  (x1  x, x2  x,
, xn  x)
2. Generate expanded simulated observations
f
yisim

H
(
x
,j
j
i, j )
Z  (y1sim  y sim , y 2sim  y sim ,
sim
, y sim

y
)
n
3. Get the coupled base vectors through SVD
E 0
C = XZ  U 
V
 0 0
T
4. Obtain the analysis state by mapping the
observations on the phase space of the model
2 S 1
attractor
x a   [  k v k T ( y o  y )]u k  x
k 1
Comparison of 4DSVD and 4DVAR
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 Experiments setup
Model: Lorenz 28-variable model
True state: Integrated the model from an artificial initial condition
Observation: Observed by adding Gaussian random noise
Sample strategy: Selected from the model outputs
Sample size: 100
Number of experiments: 30
Time window: [0, 1.0]
Experiments:
Exp.
ExpG1
ExpG2
ExpG3
ExpG4
Observation
time interval
0.1
0.2
0.5
1.0
Comparison of 4DSVD and 4DVAR
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Analysis errors of 4DSVD and 4DVAR
4DVAR
-4DSVD
RMS errors
4DVAR
RMS errors
RMS errors
4DSVD
(a)
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
(b)
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000 (c)
0.008
0.006
0.004
0.002
0.000
-0.002
-0.004
-0.006
-0.008
ExpG1
ExpG2
ExpG3
ExpG4
ExpG1
ExpG2
ExpG3
ExpG4
ExpG1
ExpG2
5
ExpG3
ExpG4
10
15
Experiment index
20
25
30
Comparison of 4DSVD and 4DVAR
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Averaged analysis errors of all the experiments
of the groups in assimilation time window.
RMS error
(a) 4DSVD
(b) 4DVAR
16 times
Non-dimensional time
Non-dimensional time
ExpG1
ExpG3
ExpG2
ExpG4
Some OSSEs using WRF model
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OSSE-1
 Experiments design
Model: Advanced Research WRF (ARW) modeling system
True state: Run the model for 24 hours started at 0600
UTC 11 May 2002, IC and BC generated from FNL
OSSE-2
Observation: Observed by adding Gaussian random noise
Analysis variable: Surface temp. (at Eta=0.9965 level)
Sample strategy: Selected from the forecast history
OSSE-3
Sample size: 150
Time window: [1200 UTC, 2400 UTC] ,12 May 2002
Experiments:
Exp.
Observation Num.
Observed Fields
Analyzed Fields
OSSE-1
2400
Surface Temp.
Surface Temp.
OSSE-2
600
Surface Temp.
Surface Temp.
OSSE-3
150
Surface Temp.
Surface Temp.
Some OSSEs using WRF model
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Analysis Fields
True State
OSSE-2
OSSE-1
OSSE-3
Some OSSEs using WRF model
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Analysis Error
OSSE_1
OSSE_2
OSSE_3
Some OSSEs using WRF model
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Domain-averaged RMSE of analyses as a
function of base vector number.
Some OSSEs using WRF model
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Table 1. The averaged errors in RMS sense of analysis
state and the optimal truncation number of all OSSEs
Experiment
Optimal RMSE
of analysis
Optimal truncation
number
OSSE-1
1.01
137
OSSE-2
1.20
60
OSSE-3
1.58
20
Conclusions and Discussions
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Conclusions:
 4DSVD is an effective and efficient DA scheme for
CDA method in simple and more real model
situations even if the observations are incomplete.
 The optimal truncation number is not only related
with the dimension of the chaotic-attractor number
but also with number of the observations
Discussions:
 Need more experiments to evaluate its performance
in real observation and real model situation
 How to determine the optimal basis vector number
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Thank you!